I'm not going to berate you for using the term "advanced", that is its own can of worms to be sure. Rather, I'm going to interpret your question as "what are some areas where New World civilizations uniquely adapted to their environment?" I hope that's okay :) Also it's been a while since I posted in this subreddit, so let's see if we can shake the dust off, hmm?

As a specialist in the Andes my knowledge of technological adaptation is more focused on South American cultures. There are several technologies I can think of just off the top of my head that certainly made life in the Andes easier for these civilizations, and which made it harder for them once the Spanish forced them to adopt European lifeways.

First, let's talk about populations, administration, and what constituted a community in the Andes. By the time of Contact, the Inca Empire had greatly expanded and institutionalized several Quechua concepts in their governance. The ayllu system of community consisted of several linked communities, often spread over several ecological zones of the drastically vertical Andes; alternately, one family could own small tracts of property in several zones. By interlinking families by marriage and sharing labor across these zones, a broad agricultural base could be established for all members of the community. The Inca systematized this approach, especially the labor-sharing aspect, by conducting the mit'a or "turn". For a portion of the year able-bodied members of a family would donate their time working on Lands of the State and Sun (royal estates), or would work on infrastructure and tributary projects for the Inca. This took the place of taxation; the only direct tribute would be in the form of crops to be stored in the local Inca storehouses for military or emergency use.

The Spanish actually re-instituted the mit'a, but not in any sustainable fashion. Once they discovered the mineral riches of Potosi and elsewhere, the mit'a was called into action in order to force laborers out of the population. However, where the Inca would subsidize this activity and do so for only a few months out of the year (often away from important moments in the agricultural cycle), the Spanish required at least six months work and often a full year, with the individual having to provide their own means to get there and subsist once arriving in town. This drastically forced relocations and abandonment of entire communities in a diaspora of indigenous cultures. Another Spanish strategy to control populations involved the forced relocation of small countryside communities into reducciones, basically little modern European towns (close to the road, easy to tax, church in the middle). This pulled families out from their land, and put them in very ecologically hazardous situations - like at the foot of a giant landslide which could bury entire towns, or in a position where entire communities could fall ill with European diseases much more rapidly due to their proximity.

I won't go on too much longer, but I will also add several architectural innovations of the Inca that were also abandoned by European colonial pressures. One of the more recognizable technologies of the Andes are the treacherous rope bridges spanning over huge rivers. Those rope bridges were part of the aforementioned infrastructural efforts of the Inca Empire in rapidly crossing their territories: the crossing of the Apurimac by the Inca was invaluable to them, as no other culture before them had done so (for instance, the Wari of a millennium earlier had to go around it, flanking the eastern edge of the Andes or traveling down to the coast). Another remarkable feat of engineering involved the Inca's stonemasonry, which hauled large stones out of quarries (often pre-formed there into blocks of a few tons) into walls that were kept together without mortar, but rather through creative joins and unique seatings for each "brick". The advantage of this mortarless wall is that it used the natural strength of the andesite rather than weakening the structural integrity of the wall by giving stresses a place to break the wall (as it would with mortar). During earthquakes (prevalent in the highlands), these foundational walls could freely shift within their seat, diffusing the energy. Once the earthquake ended, the stones only had one place to resettle - into their designed seat. Many of these walls still exist in the old Inca capital of Cusco, and have outlasted at least three earthquakes that leveled the European incarnation of the city (which preferred a Spanish layout to community planning, on grids with homes that had interior courtyards, which in earthquakes do a great job of funneling the collapsing homes directly into said courtyards).

I suppose my entire point with this is, that New World and Old World civilizations had their own adaptations for their regions of the world. Globalization and colonialism forced New World groups to abandon their adaptations for inadequate European ones, which aided in the perception that they were less technologically (or even racially) advanced than the European ones. This is perhaps one of the greatest and most terrible examples of confirmation bias ever seen in history.

I'm happy to talk more about this and provide some further reading if you like - I'm away from my books but I could probably dig something up for you.